Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Hybrid iterated local search algorithm for optimization route of airplane travel plans

The traveling salesman problem (TSP) is a very popular combinatorics problem. This problem has been widely applied to various real problems. The TSP problem has been classified as a Non-deterministic Polynomial Hard (NP-Hard), so a non-deterministic algorithm is needed to solve this problem. However, a non-deterministic algorithm can only produce a fairly good solution but does not guarantee an optimal solution. Therefore, there are still opportunities to develop new algorithms with better optimization results. This research develops a new algorithm by hybridizing three local search algorithms, namely, iterated local search (ILS) with simulated annealing (SA) and hill climbing (HC), to get a better optimization result. This algorithm aimed to solve TSP problems in the transportation sector, using a case study from the Traveling Salesman Challenge 2.0 (TSC 2.0). The test results show that the developed algorithm can optimize better by 15.7% on average and 11.4% based on the best results compared to previous studies using the Tabu-SA algorithm

Getting Things in Order: An Introduction to the R Package seriation

Seriation, i.e., finding a suitable linear order for a set of objects given data and a loss or merit function, is a basic problem in data analysis. Caused by the problem's combinatorial nature, it is hard to solve for all but very small sets. Nevertheless, both exact solution methods and heuristics are available. In this paper we present the package seriation which provides an infrastructure for seriation with R. The infrastructure comprises data structures to represent linear orders as permutation vectors, a wide array of seriation methods using a consistent interface, a method to calculate the value of various loss and merit functions, and several visualization techniques which build on seriation. To illustrate how easily the package can be applied for a variety of applications, a comprehensive collection of examples is presented.

Solving Dynamic Traveling Salesman Problem Using Dynamic Gaussian Process Regression

This paper solves the dynamic traveling salesman problem (DTSP) using dynamic Gaussian Process Regression (DGPR) method. The problem of varying correlation tour is alleviated by the nonstationary covariance function interleaved with DGPR to generate a predictive distribution for DTSP tour. This approach is conjoined with Nearest Neighbor (NN) method and the iterated local search to track dynamic optima. Experimental results were obtained on DTSP instances. The comparisons were performed with Genetic Algorithm and Simulated Annealing. The proposed approach demonstrates superiority in finding good traveling salesman problem (TSP) tour and less computational time in nonstationary conditions

The automatic design of hyper-heuristic framework with gene expression programming for combinatorial optimization problems

Hyper-heuristic approaches aim to automate heuristic design in order to solve multiple problems instead of designing tailor-made methodologies for individual problems. Hyper-heuristics accomplish this through a high level heuristic (heuristic selection mechanism and an acceptance criterion). This automates heuristic selection, deciding whether to accept or reject the returned solution. The fact that different problems or even instances, have different landscape structures and complexity, the design of efficient high level heuristics can have a dramatic impact on hyper-heuristic performance. In this work, instead of using human knowledge to design the high level heuristic, we propose a gene expression programming algorithm to automatically generate, during the instance solving process, the high level heuristic of the hyper-heuristic framework. The generated heuristic takes information (such as the quality of the generated solution and the improvement made) from the current problem state as input and decides which low level heuristic should be selected and the acceptance or rejection of the resultant solution. The benefit of this framework is the ability to generate, for each instance, different high level heuristics during the problem solving process. Furthermore, in order to maintain solution diversity, we utilize a memory mechanism which contains a population of both high quality and diverse solutions that is updated during the problem solving process. The generality of the proposed hyper-heuristic is validated against six well known combinatorial optimization problem, with very different landscapes, provided by the HyFlex software. Empirical results comparing the proposed hyper-heuristic with state of the art hyper-heuristics, conclude that the proposed hyper-heuristic generalizes well across all domains and achieves competitive, if not superior, results for several instances on all domains

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Biclustering via optimal re-ordering of data matrices in systems biology: rigorous methods and comparative studies

<p>Abstract</p> <p>Background</p> <p>The analysis of large-scale data sets via clustering techniques is utilized in a number of applications. Biclustering in particular has emerged as an important problem in the analysis of gene expression data since genes may only jointly respond over a subset of conditions. Biclustering algorithms also have important applications in sample classification where, for instance, tissue samples can be classified as cancerous or normal. Many of the methods for biclustering, and clustering algorithms in general, utilize simplified models or heuristic strategies for identifying the "best" grouping of elements according to some metric and cluster definition and thus result in suboptimal clusters.</p> <p>Results</p> <p>In this article, we present a rigorous approach to biclustering, OREO, which is based on the Optimal RE-Ordering of the rows and columns of a data matrix so as to globally minimize the dissimilarity metric. The physical permutations of the rows and columns of the data matrix can be modeled as either a network flow problem or a traveling salesman problem. Cluster boundaries in one dimension are used to partition and re-order the other dimensions of the corresponding submatrices to generate biclusters. The performance of OREO is tested on (a) metabolite concentration data, (b) an image reconstruction matrix, (c) synthetic data with implanted biclusters, and gene expression data for (d) colon cancer data, (e) breast cancer data, as well as (f) yeast segregant data to validate the ability of the proposed method and compare it to existing biclustering and clustering methods.</p> <p>Conclusion</p> <p>We demonstrate that this rigorous global optimization method for biclustering produces clusters with more insightful groupings of similar entities, such as genes or metabolites sharing common functions, than other clustering and biclustering algorithms and can reconstruct underlying fundamental patterns in the data for several distinct sets of data matrices arising in important biological applications.</p

Genetic Algorithm to Traveling Salesman Problem

In this paper, we apply a genetic algorithm to TSP. Since in TSP, a tour must pass through edges in E' ( E) at least once, it is necessary to involve E' and the information of direction in the chromosome. However, if we use the existing chromosome structure, the length of the chromosome becomes 2 jE0j and the size of the solution space becomes 2jE0j jE0j!. In the previous study, since the chromosome uses two kinds of information (E' and the direction), the results and the time to find a near-optimal solution vary according to the method of applying genetic operators. To resolve these defects, this paper proposes a new structure of chromosome for TSP

Evolutionary computation applied to combinatorial optimisation problems

This thesis addresses the issues associated with conventional genetic algorithms (GA) when applied to hard optimisation problems. In particular it examines the problem of selecting and implementing appropriate genetic operators in order to meet the validity constraints for constrained optimisation problems. The problem selected is the travelling salesman problem (TSP), a well known NP-hard problem. Following a review of conventional genetic algorithms, this thesis advocates the use of a repair technique for genetic algorithms: GeneRepair. We evaluate the effectiveness of this operator against a wide range of benchmark problems and compare these results with conventional genetic algorithm approaches. A comparison between GeneRepair and the conventional GA approaches is made in two forms: firstly a handcrafted approach compares GAs without repair against those using GeneRepair. A second automated approach is then presented. This meta-genetic algorithm examines different configurations of operators and parameters. Through the use of a cost/benefit (Quality-Time Tradeoff) function, the user can balance the computational effort against the quality of the solution and thus allow the user to specify exactly what the cost benefit point should be for the search. Results have identified the optimal configuration settings for solving selected TSP problems. These results show that GeneRepair when used consistently generates very good TSP solutions for 50, 70 and 100 city problems. GeneRepair assists in finding TSP solutions in an extremely efficient manner, in both time and number of evaluations required